All surfaces at temperatures above absolute zero give off energy in the form of electromagnetic radiation, and the rate of radiation is proportional to the fourth-power temperature of the surface. In the range of biologic and environmental temperatures, this radiation is in the form of infrared rays and visible light. The net heat exchanged between the skin surface and surrounding objects by radiation (JQ,rad) is given by the following equation:

The constant, krad, depends on the characteristics of the skin surface and the surfaces of objects in the environment to which heat is lost or from which it is gained. In general, the best radiators or acceptors of radiation are black objects, but this is less marked for infrared wavelengths, which mediate a large proportion of radiative heat exchange in the biologic temperature range. Thus, there is little difference among the races in heat exchange by infrared radiation, although heavily pigmented skin is heated largely by visible radiation, which constitutes a large fraction of the radiation energy from the sun. Although heat exchange by radiation according to Eq. [3] is determined by the 4th power of temperatures (in °K), it turns out that when the expression (T4 — Ts4) is expanded mathematically, it is approximately equal to a constant factor times Ta — Ts within the typical range of body and indoor temperatures. Thus, the rate of heat exchange by radiation can be approximated as:

In this case, k*ad is not truly a constant (it depends on the temperatures of the two surfaces to a minor degree because of the mathematical approximations made), but it varies little in any practical setting. Because the temperature difference (Ta — Ts) is the same regardless of whether it is given in °C or °K, it can be seen that the exchange of heat by radiation, like that by conduction, depends on the temperature difference between the skin surface and that of the surroundings, and it depends on the characteristics of the skin or clothing surface and those of objects in the environment.

The assumptions involved in reducing Eq. [3] to Eq. [4], however, are not accurate when the body exchanges heat with objects of significantly higher or lower temperature. The most pertinent examples are the sun and the night sky. Sunlight has an equivalent temperature of 5800°K, and, despite the fact that the sun occupies a small fraction of the area of the daytime sky, everyone is aware of its warming effect, even in cold weather. At night, when the warming radiation of the sun is absent (except the small amount reflected by the moon) and when there is no cloud cover, the night sky has a temperature of —40 to —50°C. Thus, considerable radiative heat can be lost by the body on a clear night, even in the desert.

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